How to extract only the object and get the extreme coordinates?

Dear members, I would be truly grateful if you could assist me in extracting the object indicated in the image and obtaining the coordinates of its extreme points on the right and left. My goal is to calculate the distance between these extreme points and the centroid of the object. Could you please guide me on the correct approach for achieving this?

You can find the code I am working on, the tested image and a preliminar result with the elements that I am interested.

clc
clear all
close all
set(0, 'DefaultAxesFontName', 'Times New Roman');
set(0, 'DefaultUIControlFontName', 'Times New Roman');
set(0, 'defaultUitableFontName', 'Times New Roman');
set(0, 'defaultTextFontName', 'Times New Roman');
set(0, 'defaultUipanelFontName', 'Times New Roman');
font_size = 16;
line_width_size=2;
J=zeros;
number=1;
pixelTomm=50; %Physical scale conversion factor
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%% importing Data %%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for framenumbers=53:576
% defining the range of the number of the images
close all
clear_all_but('number','framenumbers','xcentroid1','ycentroid1','xfit_Leading','yfit_Leading','Rfit_Leading','xfit_trailing','yfit_trailing','Rfit_trailing','Thetaleading','Thetatrailing')
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%% importing Data %%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
I = imread(sprintf('0000200test.jpg',framenumbers)); %Importing tif
I(:,:,3) = []; %%% removing the second and third layer of the image
I(:,:,2) = [];

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%% Plotting the original image %%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
figure(1), set(gcf,'color','w');
sz_x = 400; sz_y = 400; % size of the figure
y_pos = 600; x_pos =1; % position on the screen
set(1,'pos', [x_pos, y_pos, sz_x, sz_y]);
axes('position',[.1 .15 .8 .8]) % size of the plot in the figure
title('Original image')
figure (1)
hold on
imshow(I, []); %showing the raw image
axis on

%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%% Binarization of the image %%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
numberOfcolum = size(I, 1);% calculating the size of the raw image
numberOfrows = size(I, 2);% calculating the size of the raw image
J=zeros(numberOfcolum,numberOfrows);
% defining the matrix to store the Binarized image
for i=1:numberOfcolum
for j=1:numberOfrows
if I(i,j) < 37
%%%%%%%%%%%%%Masking the lower intensity%%%%%%%%%%
J(i,j)=0;
else
J(i,j)=1;
end
j=j+1;
end
i=i+1;
end
figure,imshow(J); %showing the black and white image
J = bwareaopen(J,20000); %Remove small objects from binary image
figure,imshow(J);
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% Detect Entire droplet and fill the hollow region %%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
[~, threshold] = edge(J, 'sobel'); %findig the edge of the bubble
fudgeFactor = .9;
BWs = edge(J,'sobel', threshold * fudgeFactor);
figure, imshow(BWs), title('binary gradient mask');
%showing the detected bubble

%%%%%%%%%%%%% Fill Interior Gaps %%%%%%%%%%%%
BWdfill = imfill(BWs, 'holes');
figure, imshow(BWdfill);
Preprocessed_Image = imcrop(BWdfill,[778.5 10.5 783 2038]);
%Cropping the original image to remove the white border
figure, imshow(BWdfill);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%% Plotting cropped image %%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
figure(2), set(gcf,'color','w');
sz_x = 400; sz_y = 400; % size of the figure
y_pos = 600; x_pos =401; % position on the screen
set(2,'pos', [x_pos, y_pos, sz_x, sz_y])
axes('position',[.1 .15 .8 .8]) % size of the plot in the figure
title('Pre-processed image')
figure(2)
imshow(Preprocessed_Image);
axis on
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% finding the centroid, leading and trailing edge of the bubble %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
stats = regionprops('table',Preprocessed_Image,'Centroid',...
'MajorAxisLength','MinorAxisLength');
xcentroid=stats.Centroid(1,1); % x of the centroid
x_centroid(number)=xcentroid; % storing x-location
ycentroid=stats.Centroid(1,2); % y of the centroid
y_centroid(number)=ycentroid; % storing y-location
MinorAxisLength=stats.MinorAxisLength(1); % length of Minor axis
MajorAxisLength=stats.MajorAxisLength(1); % length of Minor axis

Thanks!

[Walter Roberson]

Would you happen to have the original image in an image format such as png that is not lossy like jpg almost always is? JPEG lossless has trouble with sharp edges, and produces artifacts at the edges, which makes analysis more difficult.

[Rhandrey Maestri]

can it be bmp? I tried .tif but the website did not allow me to upload it

[Walter Roberson]

BMP is good.

It looks like there might be a background grid, possibly intended to help determine the sizes of objects? Is that grid 0.1mm spacing? At the moment I do not know how hard it would be to extract the grid, but if it is a known size and can be extracted, that would give us a way to calculate absolute sizes on the images instead of relative sizes.

Answer 1

[Akira Agata]

How about the following?

% Load the image
I = imread('https://jp.mathworks.com/matlabcentral/answers/uploaded_files/1552757/2000000200.bmp');

% Binarize
BW = imbinarize(I);

% Extract the ROI
BW = ~BW;
se = strel("disk", 5);
BW = imopen(BW, se);
BW = imclearborder(BW);
BW = bwareafilt(BW, 1);
BW = imfill(BW, "holes");

% Calculate the centroid
s = regionprops(BW, "Centroid");

% Calculate the extreme points
idx = any(BW);
pt1 = find(idx, 1);
pt2 = find(idx, 1, "last");

% Visualize the result
imshow(I)
hold on
xline(pt1, "r", sprintf("X = %d", pt1), "FontSize", 18)
xline(pt2, "r", sprintf("X = %d", pt2), "FontSize", 18)
h = scatter(s.Centroid(1), s.Centroid(2), "r", "filled");
legend(h, "Centroid", "FontSize", 18)

[Rhandrey Maestri]

Thanks for your great answer

[Fernando]

I does not make sense to me, how "any" function get the extremes?

[Image Analyst]

@Fernando any() gives you the linear index of all white pixels in the binary image. It is a one dimensional list. Since the list is arranged column-wise, from upper left most pixel in left most column, to lower right pixel in the right most column, it will give you the leftmost and rightmost column, though not necessarily the uppermost and lower most row. That's why I suggested bwferet

Answer 2

[Image Analyst]

Try bwferet.

help bwferet

 BWFERET Measure Feret diameters and angles of image regions.
 
   OUT = BWFERET(I) measures the maximum Feret Properties of each
   component (object) in the image. I can be a binary image, connected 
   component or labeled matrix.
 
   OUT = BWFERET(BW, PROPERTIES) measures a set of Feret properties of each
   connected component (object) in the binary image BW, which is a logical
   array.
 
   OUT = BWFERET(CC, PROPERTIES) measures a set of Feret properties of each
   connected component (object) in CC, which is a struct returned by
   BWCONNCOMP.
 
   OUT = BWFERET(L, PROPERTIES) measures a set of Feret properties of
   each labeled component (object) in the label matrix L. Positive integer
   elements of L correspond to different regions. For example, the set of
   elements of L equal to 1 corresponds to region 1; the set of elements of
   L equal to 2 corresponds to region 2; and so on.
 
   [OUT, L] = BWFERET(...) measures a set of Feret properties of each
   component (object) in the binary image, connected component or labeled
   matrix.  This also returns the corresponding label matrix L such that
   the first value in the table OUT corresponds to the labeled region
   1, the second value with the labeled region 2 and so on.
 
   PROPERTIES can be an array of strings, a single character vector, a cell
   array of character vectors, or 'all'. If PROPERTIES is set to 'all' it
   returns all the Feret properties mentioned below. If no argument is
   provided, all maximum Feret properties are given as outputs. The set of
   valid measurement strings or character vectors includes
   'MaxFeretProperties', 'MinFeretProperties' and 'all'.
 
   'MaxFeretProperties' - Outputs all the properties related to maximum 
                          Feret Diameter.
       These properties are:
       MaxDiameter    - Maximum Feret diameter length.
       MaxAngle       - Angle of maximum Feret diameter with respect to X
                        axis in degrees. The value lies between 180 to -180
                        degrees.
       MaxCoordinates - Endpoint coordinates of maximum Feret diameter.
 
   'MinFeretProperties' - Outputs all the properties related to minimum 
                          Feret Diameter.
       These properties are:
       MinDiameter    - Minimum Feret diameter length.
       MinAngle       - Angle of minimum Feret diameter with respect to X
                        axis in degrees. The value lies between 180 to -180
                        degrees.
       MinCoordinates - Endpoint coordinates of minimum Feret diameter.
 
   Class Support
   -------------
   If the first input is BW, BW must be a logical array and it should be 2D.
   If the first input is CC, CC must be a structure returned by BWCONNCOMP.
   If the first input is L, L must be real, nonsparse and 2D. L can have 
   any numeric class. The output OUT is returned as a table.
 
   Example 1
   ---------
   % Calculate the minimum Feret diameter for objects in image
   
    I = imread('toyobjects.png');
    bw = imbinarize(I, 'adaptive');
    % Retain the two biggest objects in the image
    bw = bwareafilt(bw, 2);
    bw = imfill(bw, 'holes');
    % Calculate the Feret properties of the objects in the image along with
    % the label matrix
    [out, L] = bwferet(bw, 'MinFeretProperties');
 
   Example 2
   ---------
   % Plot the maximum Feret diameter for objects in the image
   
    % Read an image
    I = imread('toyobjects.png');
    % Binarize the image
    B = imbinarize(I, 'adaptive');
    % Fill in the holes in the binary image
    B = imfill(B, 'holes');
    % Show the image
    h = imshow(B)
    ax = h.Parent;
    % Convert to connected component struct using bwconncomp
    C = bwconncomp(B);
    % Calculate Feret Properties
    F = bwferet(C, 'MaxFeretProperties');
    hold on 
    % Display maximum Feret Diameters with their values for each object
    imdistline(ax, F.MaxCoordinates{1}(:,1), F.MaxCoordinates{1}(:,2)); 
    imdistline(ax, F.MaxCoordinates{2}(:,1), F.MaxCoordinates{2}(:,2)); 
    imdistline(ax, F.MaxCoordinates{3}(:,1), F.MaxCoordinates{3}(:,2)); 
    imdistline(ax, F.MaxCoordinates{4}(:,1), F.MaxCoordinates{4}(:,2)); 
   
   See also BWCONNCOMP, BWLABEL, BWLABELN, LABELMATRIX, REGIONPROPS.

    Documentation for bwferet
       doc bwferet